American Institute of Mathematical Sciences

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August  2004, 4(3): 747-758. doi: 10.3934/dcdsb.2004.4.747

Ratio-dependent predator-prey system with stage structure for prey

Xinyu Song 1, , Liming Cai 1, and  U. Neumann 2,

1. 

Department of Mathematics, Xinyang Teachers College, Henan 464000, China, China
2. 

Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan 52900, Israel

Received  December 2002 Revised  February 2004 Published  May 2004

A ratio-dependent predator-prey model with stage structure for the prey is proposed and analyzed, which improves the assumption that each individual prey has the same ability to be captured by predator. In this paper, mathematical analysis of the model equations with regard to boundedness of solutions, nature of equilibria, permanence are analyzed. We obtain conditions that determine the permanence of the populations. Furthermore, we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model. By the application of comparing argument and exploiting the monotonicity of one equation of the model, we obtain sufficient conditions for the global attractivity of positive equilibrium.
Keywords: permanence, stability., stage structure, Ratio-dependent.
Mathematics Subject Classification: 34C05, 34D20, 92D2.
Citation: Xinyu Song, Liming Cai, U. Neumann. Ratio-dependent predator-prey system with stage structure for prey. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 747-758. doi: 10.3934/dcdsb.2004.4.747
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